An enhanced eigenvalue analysis for system dynamics models / Ahmed Farouk Mohamed Hassan Yehia ; Supervised Mohamed Mostafa Saleh

Thesis (M.Sc.) - Cairo University - Faculty of Computer and Information - Department of Operations Research and Decision Support

The main contribution of this thesis is to develop an enhanced eigenvalue analysis approach that overcomes the limitations of the traditional eigenvalue analysis via statistical association methods (measures) such as maximal information coefficient (MIC), Kernel canonical correlation analysis (KCCA) and mutual information (MI). The main limitations of the traditional eigenvalue analysis are: It conducts a univariate sensitivity analysis. It represents only the marginal contribution at a certain point. It assumes the linearity of relationships. In order to overcome these limitations, we applied the previously mentioned methods. We have faced many challenges while applying these methods, so, we did some adjustments and extensions to the methods to work around these challenges. We developed three methods, which are based on two different concepts (approaches). The first two methods are based on the mutual information concept. In the first method, we enhanced maximal information coefficient to become a multivariate method (instead of a univariate one). In the second method, we utilized the Kernel Density Estimation method to estimate the joint distribution of input and output variables, then we applied the Mutual Information concept on this joint distribution. The third method is the kernel canonical Correlation Analysis, which is based on multiple regression. The following figure summarizes our three proposed methods

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